Question

Places $A$ and $B$ are $100\mathrm{km}$ apart on a highway. one car starts from $A$ and another from $B$ at the same time. If the car travels in the same direction at different speeds, they meet in $5\mathrm{hours}$. If they travel towards each other they meet in one hour. What is the difference of speeds in $\mathrm{km}/\mathrm{hr}$ of the two cars?

Answer 1

Find the difference between the speed of two cars

Let us consider the speed of cars $A$ and $B$ are $x\mathrm{km}/\mathrm{h}\mathrm{and}y\mathrm{km}/\mathrm{h}$ respectively.

The relative speed of car travelling in the same direction $=x–y$

The relative speed of car travelling in the opposite direction$=x+y$

Distance travelled $=100\mathrm{km}$

Since when the car travels in the same direction at different speeds, they meet in $5\mathrm{hours}$.

It is represented by the equation,

$$\begin{gathered} 5(x–y)=100 \\ \therefore x-y=20...\left(1\right) \end{gathered}$$

When they travel towards each other they meet in one hour.

It is represented by the equation,

$$\begin{gathered} \therefore 1·(x+y)=100 \\ \Rightarrow x+y=100...\left(2\right) \end{gathered}$$

After solving equation $\left(1\right)\mathrm{and}\left(2\right)$.

$x=60\mathrm{km}/\mathrm{h}\mathrm{and}y=40\mathrm{km}/\mathrm{h}$

$\mathrm{Difference}\mathrm{of}\mathrm{speed}=60-40=20\mathrm{km}/\mathrm{h}$

Hence, the difference of speeds is $20\mathrm{km}/\mathrm{h}$.